64 lines
1.3 KiB
Text
64 lines
1.3 KiB
Text
/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.Tensors.Tree.Elab
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import HepLean.Tensors.ComplexLorentz.Basic
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/-!
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## The tensor structure for complex Lorentz tensors
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-/
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open IndexNotation
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open CategoryTheory
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open MonoidalCategory
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open Matrix
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open MatrixGroups
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open Complex
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open TensorProduct
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open IndexNotation
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open CategoryTheory
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noncomputable section
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namespace Fermion
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/-!
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## Example tensor trees
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-/
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open MatrixGroups
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open Matrix
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example (v : Fermion.leftHanded) : TensorTree complexLorentzTensor ![Color.upL] :=
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{v | i}ᵀ
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example :
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TensorTree complexLorentzTensor ![Color.downR, Color.downR] :=
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{Fermion.altRightMetric | μ j}ᵀ
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lemma fin_three_expand {R : Type} (f : Fin 3 → R) : f = ![f 0, f 1, f 2]:= by
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funext x
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fin_cases x <;> rfl
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open Lean
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open Lean.Elab.Term
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open Lean
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open Lean.Meta
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open Lean.Elab
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open Lean.Elab.Term
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open Lean Meta Elab Tactic
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open IndexNotation
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/-
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example : True :=
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let f := {Lorentz.coMetric | μ ν ⊗ PauliMatrix.asConsTensor | μ α β ⊗
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PauliMatrix.asConsTensor | ν α' β'}ᵀ
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have h1 : {Lorentz.coMetric | μ ν = Lorentz.coMetric | μ ν}ᵀ := by
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sorry
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sorry
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-/
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end Fermion
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end
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